Can't say how many species I have seen in captivity, but I'm very sure not as many as in the wild. Total in the wild 35 species, and here is the list:
Chalcophaps indica Asian emerald dove
Chalcophaps longirostris Pacific emerald dove
Columba guinea Speckled pigeon
Columba leucomela White-headed pigeon
Columba livia Rock pigeon
Columba palumbus European wood pigeon
Columba torringtoniae Sri Lanka wood pigeon
Ducula aenea Green imperial pigeon
Ducula pickeringii Mountain imperial pigeon
Ducula spilorrhoa Torresian imperial pigeon
Geopelia humeralis Bar-shouldered dove
Geopelia placida Peaceful dove
Geopelia striata Zebra dove
Geophaps scripta Squatter pigeon
Hemiphaga novaeseelandiae New Zealand pigeon
Leucosarcia melanoleuca Wonga pigeon
Macropygia amboinensis Brown cuckoo-dove
Macropygia unchall Barred cuckoo-dove
Ocyphaps lophotes Crested pigeon
Oena capensis Namaqua dove
Phaps chalcoptera Common bronzewing
Phaps elegans Brush bronzewing
Ptilinopus magnificus Wompoo pigeon
Spilopelia chinensis Spotted turtle-dove
Spilopelia senegalensis Laughing dove
Streptopelia capicola Ring-necked (Cape turtle-) dove
Streptopelia decaocto Eurasian collared dove
Streptopelia semitorquata Red-eyed dove
Streptopelia tranquebarica Red-collared dove
Streptopelia turtu European turtle dove
Treron bicinctus Orange-breasted green pigeon
Treron griseicauda Grey-cheeked green pigeon
Treron pompodora Sri Lankan green pigeon
Treron vernans Pink-necked green pigeon
Zenaida macroura American mourning dove
Off the top of the the head species I have seen in captivity and not in the wild include diamond dove, spinifex pigeon, Nicobar pigeon and the crowned pigeons.